Inference for Distributional Effects Using Instrumental Quantile Regression

In this paper we describe how quantile regression can be used to evaluate the impact of treatment on the entire distribution of outcomes, when the treatment is endogenous or selected in relation to potential outcomes. We describe an instrumental variable quantile regression process and the set of inferences derived from it, focusing on tests of distributional equality, non-constant treatment effects, conditional dominance, and exogeneity. The inference, which is subject to the Durbin problem, is handled via a method of score resampling. The approach is illustrated with a classical supply-demand and a schooling example. Results from both models demonstrate substantial treatment heterogeneity and serve to illustrate the rich variety of hypotheses that can be tested using inference on the instrumental quantile regression process